Answer:
the answer is approximated 83 quarters or 21 years
Explanation:
they key in this question is to take into account the word "compounded quarterly" it means that every quarter there is paid [tex]\frac{0.039}{4}=0.975\%[/tex]. So the process to obtain the answe is as follows:
[tex]3116.92*(1+0.975\%)^{n}=7000[/tex]
note here that n is the number of quarters needed for accumulating 7.000 using an interest rate of 0.975%, so we proceed with the solution
[tex]\frac{7000}{3116.92}=(1+0.975\%)^{n}[/tex]
[tex]log(\frac{7000}{3116.92})=n*log(1+0.975\%)[/tex]
Remember here the property of natural logaritm when you apply it to an exponent.
[tex]\frac{log(\frac{7000}{3116.92} )}{log(1+0.975\%)} =n[/tex]
[tex]n=83.38[/tex]
so the answer is aproximated 83 quarters or 21 years
